English Dictionary

Maclaurin series

名詞

(calculus) Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function f, the power series f(0)+(f'(0))/(1!)x+(f(0))/(2!)x²+(f'(0))/(3!)x³+⋯=∑ₙ₌₀ ᪲(f⁽ⁿ⁾(0))/(n!),xⁿ.

日本語の意味

（解析学）ある無限回微分可能な関数fについて、x=0を中心としたテイラー級数、すなわち、f(0) + (f'(0)/1!)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ⋯という形で表現される級数。

To approximate ex near zero, we use the Maclaurin series for the exponential function.

e^x を原点近くで近似するために、指数関数の原点を中心とするテイラー級数を用います。

意味（1）

(calculus) Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function f, the power series f(0)+(f'(0))/(1!)x+(f(0))/(2!)x²+(f'(0))/(3!)x³+⋯=∑ₙ₌₀ ᪲(f⁽ⁿ⁾(0))/(n!),xⁿ.

Analytically there are, of course, two Jacobi series branching off the Maclaurin series, but they are geometrically and physically identical, and involve only an interchange of a and b.

Maclaurin series （ plural ）